Question: Simplify the following expression and state the condition under which the simplification is valid: $q = \dfrac{y^2 - 7y}{y^2 - 11y + 28}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{y^2 - 7y}{y^2 - 11y + 28} = \dfrac{(y)(y - 7)}{(y - 4)(y - 7)} $ Notice that the term $(y - 7)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(y - 7)$ gives: $q = \dfrac{y}{y - 4}$ Since we divided by $(y - 7)$, $y \neq 7$. $q = \dfrac{y}{y - 4}; \space y \neq 7$